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Experimental Determination of Solubility Constants of Saponite at 1 Elevated Temperatures in High Ionic Strength Solutions, 2

Revision 1 3

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Yongliang Xiong1 5

6 Department of Nuclear Waste Disposal Research & Analysis, 7

Sandia National Laboratories (SNL), 1515 Eubank Boulevard SE, Albuquerque, NM 8 87123, USA 9

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1 Corresponding author, e-mail: yxiong@sandia.gov.

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ABSTRACT 12

Saponite occurs in a wide range of environments from hydrothermal systems on 13

the Earth to surface deposits on Mars. Of practical importance is that Mg-saponite forms 14

when glasses for nuclear waste are altered in Mg-bearing aqueous solutions. In addition, 15

saponite is favorably considered as candidate buffer materials for the disposal of high-16

level nuclear waste and spent nuclear fuel in harsh environments. However, the 17

thermodynamic properties, especially for Mg-saponites, are not well known. Here the 18

author synthesized Mg-saponite (with nitrate cancrinite) following a previously reported 19

procedure and performed solubility experiments at 80 oC to quantify the thermodynamic 20

stability of this tri-octahedral smectite in the presence of nitrate cancrinite. Then, in 21

combination with the equilibrium constant at 80 oC for the dissolution reaction of nitrate 22

cancrinite from the literature, the author determined the solubility constant of saponite at 23

80 oC based on the solution chemistry for the equilibrium between saponite and nitrate 24

cancrinite, approaching equilibrium from the direction of supersaturation, with an 25

equilibrium constant of –69.24 ± 2.08 (2s) for dissolution of saponite at 80 oC. 26

Furthermore, the author extrapolated the equilibrium constant at 80 oC to other 27

temperatures (i.e., 50 oC, 60 oC, 70 oC, 90 oC and 100 oC) using the one-term 28

isocoulombic method. These equilibrium constants are expected to find applications in 29

numerous fields. For instance, according to the extrapolated solubility constant of 30

saponite at 50 oC and 90 oC, the author calculated the saturation indexes with regard to 31

saponite for the solution chemistry from glass corrosion experiments at 50 oC and 90 oC 32

from the literature. The results are in close agreement with the experimental 33

3

observations. This example demonstrates that the equilibrium constants determined in 34

this study can be used for reliable modeling of the solution chemistry of glass corrosion 35

experiments. 36

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INTRODUCTION 38

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Saponite, a tri-octahedral smectite, occurs in a wide range of environments. For 40

instance, it occurs in igneous rocks as hydrothermal alteration products (e.g., Kohyama et 41

al., 1973; April and Keller, 1992; Garvie and Metcalf, 1997), and in metamorphosed 42

dolomitic limestone as hydrothermal products (e.g., Post, 1984). It also occurs as lake 43

sediments and in volcanic rocks on seafloor (e.g., Desprairies et al., 1989; Cuevas et al., 44

2003; Kadir and Akbulut, 2003). Its occurrence in the Martian meteorites and its 45

proposed occurrence in Mawrth Vallis region and Yellowknife Bay, Gale Crater on Mars 46

(e.g., Bishop et al., 2013; Hicks et al., 2014; Bristow et al., 2015) generated enormous 47

scientific interest. Most recently, saponite was also observed in an analog study of the 48

hydrothermal alteration in the martian subsurface (e.g., Sueoka et al., 2019; Calvin et al., 49

2020). 50

Additionally, of practical importance and therefore particular interest is that 51

saponite is relevant to the geological disposal of nuclear waste, as Mg-saponite has been 52

observed as an alteration product when a borosilicate glass for nuclear waste is corroded 53

(Thien et al., 2010) in Mg-containing solutions, as detailed below. 54

Mg-bearing groundwaters are common in the disposal concepts in various rock 55

formations. For instance, salt formations have been recommended for nuclear waste 56

isolation since the 1950’s by the U.S. National Academy of Science (1957). Because of 57

their excellent properties of high heat conduction, low permeability and a propensity to 58

self-seal, rock salt is a viable candidate for a nuclear waste repository. Salt formations 59

contain brines, which have relatively high concentrations of magnesium (Nishri et al., 60

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1988; Schussler et al., 2001; Xiong and Lord, 2008). For instance, the Q-brine at Asse, 61

Germany, has a magnesium concentration of 4.47 mol•kg–1 (Nishri et al., 1988; Schussler 62

et al., 2001). When high level waste (HLW) glass is corroded in Mg-rich brines, Mg-63

bearing phyllosilicates form as part of the secondary phase assemblage (Strachan, 1983; 64

Strachan et al., 1984; Grambow and Muller, 1989; Maeda et al., 2011). Although 65

previously, and tentatively, identified as sepiolite (a member of the palygorskite family), 66

more recent investigations have identified trioctahedral smectites, such as saponite with 67

various stoichiometries, e.g., (½Ca,Na)0.66Mg6[(Si7.34Al0.66)O20](OH)4(e.g., Abdelouas et 68

al., 1997; Thien et al., 2010; Zhang et al., 2012; Fleury et al., 2013; Debure et al., 2016; 69

Aréna et al., 2017) as a reaction product. Note that in these more recent investigations, 70

the concentration of Mg in solution is relatively low (milli-molal range), in accord with 71

the dilute nature of pore water chemical compositions recovered from silicate-dominated 72

prospective repositories (e.g., Gaucher et al., 2009). Other investigations have shown 73

that when Mg-bearing glass, such as the British Magnox compositions, is altered in dilute 74

aqueous solutions the released Mg also leads to formation of Mg-smectite phases (e.g., 75

Curti et al., 2006; Thien et al., 2012; Harrison, 2014). It is likely, therefore, that saponite 76

could be a thermodynamically stable phase that precipitates when Mg-bearing solutions, 77

both dilute and concentrated, contact silicate glass for a sufficient length of time. 78

When saponite forms, it may impact the near-field chemistry of a geological 79

repository in various rock formations including salt formations by: (1) Controlling the 80

chemical compositions, including hydrogen ion concentrations, of the contacting 81

solutions, and (2) Forming a secondary mineral assemblage that will either enhance for 82

certain periods (Lucksheiter and Nesovic, 1998; Curti et al., 2006; Fleury et al., 2013; 83

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Aréna et al., 2016, 2017), or retard (Grambow and Strachan, 1984; Frugier et al., 2005) or 84

both at different periods (Thien et al., 2012; Harrison, 2014), the dissolution rate of 85

glasses, and impact the retention of hazardous (radioactive) constituents after release 86

from the glass (e.g., Abdelouas et al., 1997). 87

In addition, because saponite has the swelling and sorption properties similar to 88

those of montmorillonite, saponite has also been proposed as a candidate buffer material 89

for HLW and spent nuclear fuel disposal in harsh environments (e.g., Yang et al., 2014). 90

This is because tri-octahedral smectites such as saponite have higher thermal and 91

chemical stabilities than di-octahedral smectites such as montmorillonite, and are less 92

susceptible to alteration in harsh environments (e.g., Eberl et al., 1978; Güven, 1990). 93

Because the phyllosilicates that form on the glass surface are typically not well 94

crystallized, and phase characterization efforts by X-ray diffraction are often technically 95

challenging, some investigators have resorted to using solution modelling to infer the 96

identity of candidate phases (c.f., Grambow and Müller, 1989). For this strategy to be 97

viable, knowledge of the thermodynamic properties of eligible phases, such as saponite, 98

is crucial. However, the thermodynamic properties of saponite, especially Mg-enriched 99

saponite, are not well-defined, and few studies have attempted to obtain them via glass 100

corrosion experiments (Aréna et al., 2017; Debure et al., 2016). For instance, in a recent 101

study, Aréna et al. (2017) tried to calculate the solubility constant of saponite (they called 102

it Mg-smectite) via geochemical modeling of their glass corrosion experiments. 103

However, their experiments were not designed, nor were they ideal, for determining the 104

solubility constants of saponite. Aluminum concentrations were very low in their 105

experiments, hampering modelling efforts. Hence, several compensating hypotheses 106

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were constructed to estimate aluminum concentrations, including: (1) that aluminium 107

concentrations were equal to the quantification limit of the instrument (ICP-AES); (2) 108

aluminum concentrations were equal to the quantification limit divided by 1000; and (3) 109

aluminium was depleted stoichiometrically from saponite. These assumptions may not 110

be warranted. 111

Without accurate knowledge of the thermodynamic properties of saponite, it is 112

difficult to make reliable and accurate predictions for the evolution of chemical 113

compositions of the solutions containing Mg interacting with glass. Accurate knowledge 114

of its thermodynamic properties is thus the prerequisite for modeling glass corrosion in 115

Mg-bearing solutions, both at high and low ionic strength. 116

The objective of this study is to determine experimentally the solubility constants 117

of hydrous saponite at elevated temperatures under well constrained conditions. The 118

author first synthesized saponite (from nitrate cancrinite) according to an established 119

methodology (see Experimental Methods). Because hydrogen ion concentrations are a 120

key parameter governing the dissolution of saponite, the author first measured pH and 121

then applied correction factors obtained at elevated temperatures (Kirkes and Xiong, 122

2018). With proper knowledge of the hydrogen ion concentrations and the 123

concentrations of Al, Mg, Na and Si in solution, the author calculated the equilibrium 124

quotients. Then, the appropriate activity coefficient model is applied to extrapolate 125

equilibrium quotients at certain ionic strengths to infinite dilution. This model allows us 126

to then assess the solubility of saponite in previously reported experiments. It is shown 127

that an accurate log K value can be used to understand glass corrosion in Mg-bearing 128

solutions under a variety of geochemical conditions. 129

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EXPERIMENTAL METHODS 131

In this study, the chemicals used for synthesis of the starting material were ACS 132

reagent grade chemicals. The synthesis followed the procedure of Shao and Pinnavai 133

(2010) with some modifications. In the work of Shao and Pinnavai (2010), the sources 134

for Al, Mg, Na and Si, were Al(NO3)3•9H2O, Mg(NO3)2•6H2O, and water glass solution 135

(containing 27 wt.% Si and 14 wt.% NaOH), respectively. In this work, the source for Si 136

is Na2SiO3•9H2O, and NaOH was used to control the pHm conditions. Other reagents are 137

the same as those in Shao and Pinnavai (2010). Deionized water (DI) with >18.3 MΩ·cm 138

used in the experiments was purged with high purity Ar gas for a minimum of one hour 139

to remove dissolved CO2, following the procedure of Wood et al. (2002) and Xiong 140

(2008). 141

A supersaturation experiment was conducted at 80.0 ± 0.5 oC as follows. First, 142

the author synthesized a mixture of saponite and nitrate cancrinite at 90 oC following the 143

procedure of Shao and Pinnavai (2010). The author kept the synthesized solid mixture 144

together with the mother solution in the same container in an oven at 90 oC for 7 days. 145

Then, the author transferred the container to another oven at 80 oC. Because aluminum 146

silicates such as zeolites exhibit prograde solubility (i.e., higher solubility at higher 147

temperatures) (Xiong, 2013), it is considered that the experiment initially kept at 90 oC 148

for some time, and then remained at 80 oC, approaches the equilibrium from the direction 149

of supersaturation. 150

Solution samples were periodically withdrawn from the experiments. Before each 151

sampling, pH readings were taken for each experiment. In each sampling, about 3 mL of 152

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solution was taken from each experiment, and the solution samples were filtered through 153

a 0.2 µm filter, and transferred into pre-weighed 10 mL Grade A volumetric flasks. After 154

filtration, masses of each solution sample were determined with a balance that is precise 155

to the fourth decimal place. Samples were then immediately acidified with 0.5 mL of the 156

Optima® Grade concentrated HNO3 from Fisher Scientific, and diluted to 10 mL with DI 157

water. Chemical analyses for sodium, magnesium, aluminum, and silica were performed 158

using a PerkinElmer Optima 8300 Dual View (DV) ICP-AES. 159

The pH readings were measured with an Orion-Ross combination pH glass 160

electrode, coupled with an Orion Research EA 940 pH meter that was calibrated with 161

three pH buffers (pH 4, pH 7, and pH 13) at the experimental temperature of 80 ± 0.5oC. 162

The pH scale used in this work is the concentration scale (Mesmer and Holmes, 1992), 163

denoted as pHm, which is a negative logarithm of hydrogen ion concentration on a molal 164

scale. The pH readings are converted to pHm, according to the following equation (Xiong 165

et al., 2010), 166

167

pHm = pHob + Am = pHob + AM – log Q 168

169

where Am and AM are correction factors on a molal scale and a molar scale, respectively, 170

and Q is a conversion factor from molality to molarity. In this study, the expression of 171

correction factors as a function of ionic strength at 80 oC determined for NaCl solutions 172

from Kirkes and Xiong (2018) is used to calculate the correction factors for the ionic 173

strengths of the experiment. 174

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Solid phases were analyzed using a Bruker D8 Advance X-ray diffractometer 175

with a Sol-X detector. XRD patterns were collected using CuKa radiation at a scanning 176

rate of 0.667o/min for a 2q range of 10–90o. 177

Major elemental compositions (Na2O, Al2O3, MgO and SiO2) of the saponite 178

crystals were determined by electron microprobe analysis (EMPA) at Sandia National 179

Laboratory, Albuquerque. Analyses were obtained using a JEOL JXA-8530F hyperprobe 180

electron probe micro analyzer with a field emission electron gun. The beam conditions 181

were <1 µm spot size, 15 keV accelerating potential and a current of 20 nanoamps. 182

Concentrations (wt.% oxide) were determined using Wavelength Dispersive 183

Spectrometry (WDS) to count on separate X-ray peaks judiciously chosen for efficiency, 184

performance and lack of interference. Background offsets were chosen at least 500 steps 185

away from the peak centers. Concentrations were quantified by comparing counts from 186

simple silicate standards whose chemical compositions are known. A table that lists the 187

element, the lower limit of detection, or LLD (wt. %), the crystal diffractometer and the 188

counting times is provided (Appendix A). 189

Concentrations of the major elements in saponite were determined by averaging 190

27 points. Adsorbed water was determined by loss on ignition (LOI) by heating a sample 191

to 700 °C for one hour using a Netzsch STA 409 thermal gravimetric analyzer (TGA). 192

The chemical formula of the saponite was calculated on the basis of O20(OH)4 per 193

formula unit. 194

SEM and EDS analyses were performed using a JEOL JSM-5900LV scanning 195

electron microscope (SEM) imaging system coupled with a NORAN System 7 Spectral 196

Analysis System for energy dispersive spectroscopy (EDS). 197

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RESULTS 199

XRD pattern of the synthesized saponite is presented in Figure 1. As is shown, 200

this pattern is in reasonable agreement with that for saponite 15Å (PDF 00-013-0086) 201

(Figure 1). Notice that saponite 15Å is a pure end-member of magnesium saponite with a 202

chemical formula of Mg3(Si, Al)4O10(OH)2•4H2O. The peak at 2q ~60o, characteristic of 203

saponite, is present in the saponite synthesized in this work (Figure 1), which was also 204

observed in saponite synthesized at 160 oC by other researchers (i.e., He et al., 2014). 205

The d-spacings of the major peaks for the synthesized saponite compare well with those 206

of saponite 15Å standard (see Appendix B). In the synthesized saponite, there are some 207

concentrations of sodium, as indicated by EMPA (Table 1) and SEM-EDS analyses 208

(Figure 2). As my synthesis method follows that of Shao and Pinnavaia (2010), in which 209

it was known that there was nitrate cancrinite in addition to saponite, the two extra peaks 210

at 2q = 13.97o and 27.48o in Figure 1 can be attributed to nitrate cancrinite (Hund, 1984; 211

Liu et al., 2005). 212

Interestingly, the flower-like morphology of the synthetic saponite produced in 213

this study (see Figure 2A, 2B, 2C), is very similar to that observed for saponite 214

precipitated on the surface of vitrified intermediate level nuclear waste corroded in a 215

calcium-rich, magnesium-bearing solution (see Figure 4b in Utton et al., 2013). The 216

saponite in Utton et al. (2013) has a general formula of 217

Ca0.25(Mg,Fe)3[(Si,Al)4O10](OH)2•n(H2O). The calcium in the saponite reported in Utton 218

et al. (2013) comes from the high Ca solutions that reacted with glass. In the corrosion 219

experiments of the nuclear waste glass in 0.016 mol•kg–1 MgCl2 at 50 oC performed by 220

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Thien et al. (2010), the morphology of the corrosion product saponite (see Figure 1 in 221

Thien et al., 2010) is also similar to that of the synthetic saponite in this study. In Thien 222

et al. (2010), the stoichiometry of the saponite is 223

Na0.39(Mg2.25Li0.06Al0.06Fe0.06M0.25)[(Si3.23Al0.77)O20](OH)4, where M is a cation as Ni2+ or 224

Mn2+. This stoichiometry is similar to that of the saponite synthesized in this study (see 225

below). 226

According to EPMA analysis, the stoichiometry of saponite synthesized in this 227

work is Na0.95(Mg5.90Al0.06)[(Si7.07Al0.93)O20](OH)4. The structural formula is calculated 228

by normalizing cation compositions to a theoretical structure containing O20(OH)4. The 229

total weight loss (loss on ignition, LOI) up to 700 oC is 19 wt%, similar to that for the 230

natural saponite from California (Post, 1984), which has a total weight loss of 16.66 wt% 231

(Table 1). The stoichiometry of the natural saponite from Ballarat, California, is 232

calculated as (Ca,Na,K)0.75(Mg5.17Al0.31FeIII0.13)[(Si7.55Al0.45)O20](OH)4 (Table 1). The 233

natural saponite from Milford, Utah, has a LOI of 17.30 wt% (Cahoon, 1954), and its 234

stoichiometry is calculated as (Ca,Na,K)0.42(Mg5.72Al0.19FeIII0.02) [(Si7.50Al0.50)O20](OH)4 235

(Table 1). In addition, the stoichiometry of the natural saponite from Allt Ribhein, Skye, 236

is (Ca,Na, K)1.02(Mg5.84, Mn0.01, Al0.03, FeIII0.08)[(Si6.99Al1.01)O20](OH)4 (MacKenzie, 237

1957) (Table 1). Therefore, the stoichiometry of natural saponite varies to some degree. 238

The stoichiometric coefficients for Mg are similar in saponite from these localities, 239

suggesting they belong to Mg-saponite. Notice that the stoichiometry of the synthetic 240

saponite is similar to that from Allt Ribhein, Skye, in terms of Si, Al, and Mg. 241

In this study, the solubility experiment at 80 ± 0.5 oC was performed from the 242

direction of supersaturation to approach equilibrium (see Experimental Methods section 243

13

for details). The experimental results for pHm, sodium, total magnesium, total aluminum, 244

total silica, nitrate and hydroxyl concentrations are presented in Table 2 and are displayed 245

in Figure 3. It is clear from Figure 3 that steady state conditions were achieved for all 246

solutes in terms of concentration with deviations generally ≤ 25% on a linear scale. For 247

instance, the sodium concentrations remain between 1.38 and 1.44 mol•kg–1, a deviation 248

of 4%. Note that Al and Si usually vary reciprocally for the dissolution of Al-silicates, 249

and it is appropriate to assess their variations using the solubility product of both Al and 250

Si (i.e., mSAl × mSSi) (Xiong, 2016). As nitrate cancrinite and saponite are in equilibrium 251

in our experiment, the equilibrium constant for the assemblage of nitrate cancrinite and 252

saponite can be determined, based on the experimental results. 253

The equilibrium between saponite and nitrate cancrinite in alkaline solutions can 254

be written as follows: 255

256

Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 2NO3– + 7.05Na+ + 5.01Al(OH)4– 257

Na8[Al6Si6O24](NO3)2•4H2O + 5.90Mg2+ + 9.62OH– + 1.07H2SiO42– + 2.14 H2O(l) 258

(1) 259

The equilibrium quotient for Reaction (1) is: 260

261

(2) 262

263

The equilibrium constant at infinite dilution is: 264

265

2 22 4

3 4

5.90 1.07 9.62

1 7.05 2 5.01( )

( ) ( ) ( )

( ) ( ) ( )Mg H SiO OH

Na NO Al OH

m m mQ

m m m+ - -

+ - -

´ ´=

´ ´

14

(3) 266

267

In the above equations, mi denotes a concentration for the i-th species on a molal scale, 268

mol•g–1; gi an activity coefficient for the i-th species; and aH2O activity for water. The 269

equilibrium quotient for Reaction (1) at 80 oC is listed in Table 3. 270

Similarly, the dissolution reaction for nitrate cancrinite in alkaline solutions can 271

be expressed as: 272

273

Na8[Al6Si6O24](NO3)2•4H2O + 12OH– + 8H2O(l) 274

8Na+ + 6Al(OH)4– + 6H2SiO42– + 2NO3– (4) 275

The equilibrium quotient for Reaction (4) can be expressed as: 276

277

(5) 278

279

The corresponding equilibrium constant at infinite dilution is: 280

281

(6) 282

283

Bickmore et al. (2001) determined a value of = –36.2 ± 0.6 (2s) for 284

Reaction (4) at 89 oC. Lichtner and Felmy (2003) provided a value of = –39.03 285

2 2 22 4

3 4

5.90 1.07 9.62 2.1401 1 7.05 2 5.01

( )

( ) ( ) ( ) ( )

( ) ( ) ( )H OMg H SiO OH

Na NO Al OH

aK Q

g g g

g g g+ - -

+ - -

´ ´ ´= ´

´ ´

23 4 2 4

8 2 6 6( )

4 12

( ) ( ) ( ) ( )

( )Na NO Al OH H SiO

OH

m m m mQ

m+ - - -

-

´ ´ ´=

23 4 2 4

2

8 2 6 6( )0

4 4 12 8

( ) ( ) ( ) ( )

( ) ( )Na NO Al OH H SiO

H OOH

K Qa

g g g g

g+ - - -

-

´ ´ ´= ´

´

010log K

010log K

15

at 75 oC. The linear interpolation of these two values leads to a value of –37.99 ± 0.70 286

(2s) for Reaction (4) at 80 oC (Table 3). This value is used to retrieve the solubility 287

constant for saponite at 80 oC as detailed below. 288

In our thermodynamic calculations for the activity coefficients for Equations (3) 289

an (6), we use the computer code EQ3/6 Version 8.0a (Wolery et al., 2010; Xiong, 2011). 290

In all calculations, the activity of all solid phases is assumed to be unity. The EQ3/6 code 291

has been successfully used as a modeling platform in a number of previous studies at 292

ambient temperature (e.g., Xu et al., 1999; Kong et al., 2013; Xiong, 2015, 2020) and at 293

elevated temperatures up to 523.15 K (e.g., Xiong, 2013, 2014, 2016). 294

The database used for thermodynamic calculations is DATA0.YPF (Wolery and 295

Jarek, 2003), which utilizes the Pitzer model for calculations of activity coefficients of 296

aqueous species. The database was modified with the addition of the Pitzer parameters 297

and equilibrium constants for Al and Si species from Xiong (2013 and 2014). 298

Based on the experimental data, we first calculated the equilibrium constant for 299

Reaction (1) (Table 3). The equilibrium constant for Reaction (1) at infinite dilution and 300

80 oC is –31.25 ± 1.96 (2s) in logarithmic units (Table 3). 301

The combination of Reactions (1) and (4) leads to, 302

303

Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 2.38OH– + 5.86H2O(l) 304

0.95Na+ + 5.90Mg2+ + 0.99Al(OH)4– + 7.07H2SiO42– (7) 305

306

The equilibrium quotient for Reaction (7) can be expressed as: 307

308

16

(8) 309

310

The corresponding equilibrium constant at infinite dilution is: 311

312

(9) 313

314

According to the equilibrium constants for Reactions (1) and (4), the equilibrium constant 315

for dissolution of saponite at 80 oC in alkaline solutions (i.e., pHm ~12.58), represented 316

by Reaction (7), is computed to be –69.24 ± 2.08 (2s) in logarithmic units (Table 3). The 317

quoted uncertainty includes the error propagations. 318

319

DISCUSSIONS 320

Debure et al. (2016) conducted three glass corrosion experiments with the 321

International Simple Glass (GISG) at 90 oC. The first one involved pure water, the second 322

experiment used 8×10–3 mol•dm-3 MgCl2 as the Mg-source, and the third corrosion 323

experiment was conducted in the presence of hydromagnesite. In their experiments with 324

MgCl2 and hydromagnesite, it was observed that Mg-phyllosilicates (saponite) were 325

formed as white crusts on the glass powder surface, whereas no Mg-phyllosicates were 326

observed in the experiment with pure water. Because, for their corrosion experiment 327

with hydromagnesite, they determined a complete set of chemical compositions for the 328

solution, that experiment is an appropriate candidate to test the solubility constant of 329

2 24 2 4

0.95 5.90 0.99 7.07( )

7 2.38

( ) ( ) ( ) ( )

( )Na Mg Al OH H SiO

OH

m m m mQ

m+ + - -

-

´ ´ ´=

2 24 2 4

2

0.95 5.90 0.99 7.07( )0

7 7 2.38 5.86

( ) ( ) ( ) ( )

( ) ( )Na Mg Al OH H SiO

H OOH

K Qa

g g g g

g+ + - -

-

´ ´ ´= ´

´

17

saponite determined in this study. In the test, this author calculates the saturation index 330

for saponite at 90 oC with the stoichiometry determined in this study for the experimental 331

solution in Debure et al. (2016) at the same temperature. 332

In the calculations, the author first extrapolated the solubility constant of saponite 333

determined at 80 oC to the experimental temperature of 90 oC in Debure et al. (2016). In 334

the extrapolation, the author uses the one-term isocoulombic approach (Gu et al., 1994) 335

for the following semi-isocoulombic reaction, utilizing ionization of water as a model 336

substance to balance the charges for the reaction: 337

338

Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 15.13OH– + 12.75H+ 339 0.95Na+ + 5.90Mg2+ + 0.99Al(OH)4– + 7.07H2SiO42– + 5.86H2O (l0) 340 341 The transformation to the above semi-isocoulombic reaction is achieved by 342

combination of Reaction (7) with the following reaction, 343

344

12.75 × [H2O(l) = H+ + OH–] (11) 345

346

In the one-term isocoulombic approach for extrapolation, the equilibrium 347

constants for Reaction (10) at the temperatures of interest are first calculated. Then, the 348

solubility constants for saponite for Reaction (7) at the respective temperatures are 349

retrieved by adding the equilibrium constants for Reaction (11) to those for Reaction 350

(10). The equilibrium constants for Reaction (11) at the temperatures of interest are 351

taken from EQ3/6 database, DATA0.YPF. The extrapolated solubility constants for 352

saponite at temperatures close to 80 oC obtained in this way are listed in Table 4. 353

18

The saturation index, for the experimental solution of Debure et al. (2016) (see 354

their Table 3) at 90 oC is calculated (Table 5) with the solubility constant of saponite at 355

90 oC. Note that the chemical composition of my synthesized saponite is similar to that 356

reported by Debure et al. (2016) (“Phyllosilicate-Mg A”; see their Table 7). The 357

calculated saturation index is 0.54, indicating that the solution is saturated or slightly 358

supersaturated with saponite (Table 5). This is in good agreement with the experimental 359

observations that Mg-phyllosilicate did form in their experiment. As mentioned above, 360

the calculated saturation index is 0.54 (Table 5). Statistically speaking, the predictions 361

could encompass the exact saturation when the uncertainty associated with the solubility 362

constant of saponite at 90 oC (–67.6 ± 2.5, Table 4) is taken into consideration. 363

Thien et al. (2012) conducted glass corrosion experiments in synthetic ground 364

water (SGW) at 50 oC relevant to geological disposal of HLW. The SGW has the 365

chemical compositions that represent the ground water in equilibrium with the Callovo-366

oxfordian argillite formation at Bure underground laboratory. The glasses they used were 367

AVM 6 and AVM 10 glasses; both of them containing magnesium as one of the 368

components. The AVM 6 glass was more enriched in SiO2 than the AVM 10 glass. The 369

Mg-phyllosilicate (saponite) was precipitated in their experiments involving the AVM 6 370

glass. 371

Using the extrapolated solubility constant for saponite at 50 oC (Table 4), the 372

author calculated the saturation index for the experimental compositions of Thien et al. 373

(2012) involving the AVM 6 glass with the SGW at 50 oC. The calculated saturation 374

index is 0.71 (Table 6), indicating that saponite has a thermodynamic driving force for its 375

19

formation from the experimental solution. This is consistent with the experimental 376

observations. 377

IMPLICATIONS AND CONCLUDING REMARKS 378

One important implication from this study is that when a nuclear waste glass is 379

corroded in Mg-bearing solutions, Mg-saponite forms as a corrosion product, and the 380

resulting solutions are close to be in equilibrium with Mg-saponite. Therefore, the 381

solubility constants of Mg-saponite should be in the database as an essential part for 382

prediction of the corrosion rates as a function of the solution chemistry in equilibrium 383

with Mg-saponite. 384

Wilson et al. (2006) used the method proposed by Vieillard (2000) to estimate the 385

Gibbs free energies of formation for smectites including Na-saponite with the 386

stoichiometry of Na0.70(Mg6.00)[(Si7.30Al0.70)O20](OH)4. Notice that Wilson et al. (2000) 387

used O10(OH)2 per formula unit for Na-saponite. To be consistent with O20(OH)4 per 388

formula unit used in this study, their values are converted to those referring to O10(OH)2 389

per formula unit. They calculated the equilibrium constants for the dissolution of Na-390

saponite according to the following reaction, 391

392

Na0.70(Mg6.00)[(Si7.30Al0.70)O20](OH)4 + 14.8H+ 0.70Na+ + 6 Mg2+ 393

+ 0.70Al3+ + 7.30SiO2(aq) + 9.4H2O(l) (12) 394

395

The for Reaction (12) at 80 oC estimated by Wilson et al. (2006) is 50.95 396

(uncertainty not provided, and the same is true with the following citations of the values 397

from Wilson et al., 2006). The stoichiometry of their Na-saponite is very close to that of 398

010log K

20

the saponite studied in this work, and therefore their estimated value can be compared 399

with the value determined in this study. In order to do a direct comparison with the 400

equilibrium constant at 80 oC determined in this study, Reaction (7) is transformed into 401

the following form, 402

403

Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 15.72H+ 0.95Na+ + 5.90Mg2+ 404 405

+ 0.99Al3+ + 7.07SiO2(aq) + 9.86H2O(l) (13) 406 407

by combining Reaction (7) with the following reactions, 408

409

H2O(l) = H+ + OH– (14) 410

411

SiO2(aq) + 2H2O(l) = 2H+ + H2SiO42– (15) 412

413

Al3+ + 4H2O(l) = Al(OH)4– + 4H+ (16) 414

415

The equilibrium constants for Reactions (14) through (16) are from the EQ3/6 Data0.YPF 416

database, Xiong (2013), and Xiong (2014), respectively. Accordingly, the for 417

Reaction (13) at 80 oC is 70.30 ± 2.08. The estimated by Wilson et al. (2006) 418

differs from the experimentally determined value by ~20 orders of magnitude. 419

The estimated for Reaction (12) at 90 oC is 48.75 (Wilson et al. 2006), in 420

comparison with the extrapolated of 70.8 ± 2.5, based on the experimentally 421

010log K

010log K

010log K

010log K

21

determined value. When the estimated is used to calculate the saturation index 422

( ) of saponite for the solution chemistry from Debure et al. (2016) at 90 oC, the 423

saturation index is too high ( > 12) to be consistent with the experimental 424

observations. Similarly, the estimated for Reaction (12) at 50 oC is 58.35 425

(Wilson et al. 2006), whereas the extrapolated is 70.4 ± 2.5. When the 426

estimated is applied to the solution chemistry at 50 oC from Thien et al. (2012), 427

the saturation index is too high ( > 12) to be consistent with the experimental 428

observations. Consequently, in light of the experimental results presented in this work, 429

the estimation method needs to be revised to reconcile with the experimentally 430

determined values of this work and the experimental observations of Thien et al. (2012) 431

and Debure et al. (2016). 432

In addition, there is a solid phase of saponite-Na in the ThermoChimie database 433

(Giffaut et al., 2014; Blanc et al., 2015). The saponite-Na in the database has the 434

following stoichiometry on the basis of O20(OH)4 per formula unit: 435

Na0.68(Mg6.00)[(Si7.32Al0.68)O20](OH)4. The solubility constant ( ) for dissolution 436

of the saponite-Na at 25 oC according to the following reaction 437

Na0.68(Mg6.00)[(Si7.32Al0.68)O20](OH)4 + 14.72H+ 0.68Na+ + 6 Mg2+ 438

+ 0.68Al3+ + 7.32H4SiO4(aq) + 9.4H2O(l) (12) 439

is 57.28 ± 7.30 based on the data set of 10a Version of September 26, 2018 (ANDRA, 440

2021). Notice that the error estimates are calculated based on the error percentage 441

010log K

log QK

log QK

010log K

010log K

010log K

log QK

010log K

22

relative to the basis of O10(OH)2 per formula unit in the original data set. The 442

extrapolated value at 25 oC for Reaction (13) is 72 ± 5, based on the value listed in 443

Table 4 in this study. When the quoted uncertainties and differences in stoichiometry are 444

taken into consideration, the estimated value from the ThermoChimie can be considered 445

to agree with the experimentally-based value at 25 oC. This is encouraging for the 446

estimation method, and it can be recalibrated with the experimental data at 25 oC 447

obtained in this study. In this way, the estimation method will be better to reconcile with 448

the experimental data and experimental observations, especially at elevated temperatures, 449

noted for the comparisons with the estimated values from Wilson et al. (2006), as the 450

ThermoChimie database and Wilson et al. (2006) use the same or very similar estimation 451

method. 452

In summary, the solubility constant of saponite with a stoichiometry of 453

Na0.95(Mg5.90Al0.06)[(Si7.07Al0.93)O20](OH)4 at 80 oC has been determined in this work. 454

Then, the author extrapolated this value to other temperatures close to 80 oC (i.e., 50 oC, 455

60 oC, 70 oC, 90 oC, and 100 oC) by employing the one-term isocoulombic approach. The 456

author calculated the saturation indexes, , for the solution chemistry from the glass 457

corrosion experiments in the presence of a Mg-source at 50 oC and 90 oC from different 458

researchers. My calculated saturation indexes suggest that the solutions are 459

saturated/slightly-supersaturated with saponite, which are in close agreement with the 460

experimental observations at various temperatures. This suggests that the alteration 461

products containing Mg formed when glasses are corroded in a solution in the presence of 462

a Mg-source may control the chemical compositions, including hydrogen ion 463

concentrations, of the solutions in contact with the glasses. As the compositions of 464

log QK

23

natural saponite vary to some degree, the results are best applied to the situations where 465

the compositions of saponite are similar to those of synthetic saponite, such as the 466

saponite from Allt Ribhein, Skye. 467

468

Acknowledgements 469

Sandia National Laboratories is a multi-mission laboratory operated by National 470

Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of 471

Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear 472

Security Administration under contract DE-NA-0003525. This research is funded by Salt 473

R&D programs administered by the Office of Nuclear Energy (NE) of the U.S 474

Department of Energy. The views expressed in the article do not necessarily represent 475

the views of the U.S. Department of Energy or the United States Government. This paper 476

is published with the release number SAND2019-3740J. The author gratefully 477

acknowledges the laboratory assistance from Leslie Kirkes, Jandi Knox, Cassie Marrs, 478

Heather Burton, and Dick Grant. The author is grateful to the two journal reviewers for 479

their insightful and thorough reviews. Their reviews helped to improve the manuscript 480

significantly. The author thanks the Associate Editor (AE), Dr. Daniel Neuville, for his 481

editorial efforts, and the Editor, Dr. Hongwu Xu, for his editorial comments and his time. 482

483

484

24

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682

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Figure Captions 683 684 685 Figure 1. XRD pattern of the solubility-controlling phases in the experiment performed 686 in this work, compared with those of saponite 15A and NO3-cancrinite. 687 688 689 Figure 2. SEM images and EDS analyses for the solid phases from the experiment 690 performed in this study. A–C are SEM images with the respective EDS analyses: A. 691 magnification at 6,500 times; B. magnification at 5,500 times; and C. magnification at 692 3,700 times. 693 694 695 Figure 3. A plot showing total molal concentrations of Al(III), Mg(II), Na(I), NO3–, and 696 Si(IV) as a function of experimental time in an experiment approaching equilibrium from 697 the direction of supersaturation at 80 oC. 698 699 700 701 702 703

704

30

705 Table 1. Chemical compositions of saponite synthesized in this work in comparison with 706

those of natural saponite. 707 708 709

Oxide

Synthetic Saponite, This Work, wt%

Natural Saponite, Ballarat,

California, wt% A

Natural Saponite, Milford,

Utah, wt% B

Natural Saponite, Allt Ribhein, Fiskavaig Bay, Skye, wt% C

SiO2 46.80 51.26 50.01 43.62 TiO2 0.00 0.09 0.00 0.00 Al2O3 5.56 4.42 3.89 5.50 Fe2O3 0.00 1.14 0.21 0.66 FeO 0.00 --- 0.00 --- MnO 0.00 0.03 0.00 0.06 MgO 26.22 23.54 25.61 24.32 CaO 0.00 1.25 1.31 2.85 Na2O 3.27 1.14 0.00 0.08 K2O 0.00 0.18 0.00 0.04 H2O (LOI) 19.26 D 16.66 17.30 22.90

710 A Post (1984), (Ca,Na,K)0.75(Mg5.17Al0.31FeIII0.13)[Si7.55Al0.45]O20(OH)4. The 711

stoichiometry is calculated in this work on the basis of O20(OH)4 per formula unit. 712 713 B Cahoon (1954), (Ca,Na,K)0.42(Mg5.72Al0.19FeIII0.02) [Si7.50Al0.50]O20(OH)4. The 714

stoichiometry is calculated in this work based on O20(OH)4 per formula unit.. 715 716 C Mackenzie (1957), (Na, K, Ca)1.02(Mg5.84, Mn0.01, Al0.03, FeIII0.08)Si6.99Al1.01O20(OH)4. 717

The stoichiometry was calculated by Mackenzie (1957). I obtained almost the same 718 formula based on the compositions provided. 719

720 D Based on TGA analysis up to 700 oC. 721 722 723

724

31

725 Table 2. Experimental data from the solubility experiment regarding the equilibrium 726

between nitrate cancrinite and saponite produced in this study at 80.0 ± 0.5 oC. 727 728

Experimental Number

Experimental time, days ApHm BmNa

BmSMg(II)

BmSAl(III) BmSSi(IV) CmNO3

- DmOH- SAP-80-1 64 12.58 1.38 1.24E-05 2.94E-04 1.66E-02 6.72E-01 0.674 85 12.56 1.42 1.11E-05 2.78E-04 1.99E-02 7.01E-01 0.674 92 12.61 1.44 1.50E-05 1.94E-04 3.51E-02 6.91E-01 0.674 A Measured pH readings at 64, 85, 92 days were 12.43, 12.40, and 12.45, respectively, at 729

the experimental temperature. The pHm values are calculated by applying the 730 correction factor at 80 oC from Kirkes and Xiong (2018) at the ionic strength of the 731 experiment. 732

B Analyzed with ICP-AES 733 C Calculated based on charge balance 734 D Based on the initial NaOH concentration. 735 736 737

738

32

739 Table 3. Equilibrium constants of saponite at 80 ± 0.5 oC determined in this work 740

741 Reactions log10 QA log10 K0 Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 2NO3– + 7.05Na+ + 5.01Al(OH)4– Na8(Al6Si6O24](NO3)2•4H2O + 5.90Mg2+ + 9.62OH– + 1.07H2SiO42– + 2.14H2O(l) (1)

–23.52 ± 1.96 (2s)

–31.25 ± 1.96 (2s)

Na8(Al6Si6O24](NO3)2•4H2O + 12OH– + 8H2O(l) 8Na+ + 6Al(OH)4– + 6H2SiO42– + 2NO3– (4)

–37.99 ± 0.70 (2s) B

Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 2.38OH– + 5.86H2O(l)

0.95Na+ + 5.90Mg2+ + 0.99Al(OH)4– + 7.07H2SiO42– (7) –69.24 ±

2.08 (2s) C A At ionic strength of 1.4 mol•kg–1 742 743 B Based on a linear interpolation of the values at 89 oC (–36.20) from Bickmore et al. 744

(2001) and at 75 oC (–39.03) from Lichtner and Felmy (2003). 745 746 C A combination of the reaction in Row 2 with that in Row 3 leads to the reaction in Row 747

4 and its corresponding equilibrium constant. 748 749 750

Table 4. Extrapolated equilibrium constants of saponite with the stoichiometry 751 determined in this work at other temperatures close to 80oC 752

753 Reactions T oC log10 K0 25 –80 ± 5 C 50 –74.7 ± 2.5 C 60 –72.8 ± 2.5 C Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4 + 2.38OH– + 5.86H2O(l)

0.95Na+ + 5.90Mg2+ + 0.99Al(OH)4– + 7.07H2SiO42– 70 –70.96 ± 2.5 B

80 –69.24 ± 2.08 (2s) A 90 –67.6 ± 2.5 C 100 –66.1 ± 2.5 C

A Determined in this study. 754 B One-term isocoulombic extrapolation based on the experimental value at 80 oC. 755 C Linear extrapolation in the space of log K vs. 1/T where T is in absolute temperature in 756

K, based on the values at 70 oC and 80 oC. 757 758 759

760

33

Table 5. Chemical compositions of the solution in which the international simple glass 761 was corroded at 90 oC 762

Concentration SSi SB SNa SAl SCa SMg mmolar A

1.49E+00 1.1561E+02 6.298E+01 6.00E-

02 5.00E-

02 5.00E-

02 mmolal B

1.55E+00 1.20E+02 6.55E+01 6.24E-

02 5.20E-

02 5.20E-

02 Saturation state with respect to saponite, Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4

C 0.5367

A From Debure et al. (2016); concentration unit, 10–3 mol•dm–3. 763 B This study, concentration unit, 10–3 mol•kg–1. Converted from the results from Debure 764

et al. (2016) by using a density of 0.15 mol•dm–3 NaCl at 90 oC to approximate the 765 density of the experimental solution in Debure et al. (2016). The density of 0.15 766 mol•dm–3 NaCl at 90 oC is from Sőhnel and Novotný (1985). 767

C In , Q is ion activity product (IAP) with respect to saponite; K is the equilibrium 768

constant defined by Reaction (7). In the calculation, pH was assumed to be constrained 769 by the charge balance. 770 771 772 773 774

775

log QK

log QK

34

776 Table 6. Chemical compositions of the solution in which the AVM 6 nuclear glass was 777

corroded in synthetic groundwater (SGW) at 50 oC 778 Concentration SSi SB SNa SLi SAl

mg/L A 19 786 2257 24 1.9 molar B 6.77E-04 7.27E-02 9.82E-02 3.46E-03 9.06E-05 molal C 6.86E-04 7.38E-02 9.96E-02 3.51E-03 9.19E-05

Concentration SMg SK SCa SCl SSO4 mg/L A 16 45 30 1491 1397 molar B 6.58E-04 1.15E-03 7.49E-04 4.21E-02 1.45E-02 molal C 6.68E-04 1.17E-03 7.59E-04 4.27E-02 1.48E-02

Saturation state with respect to saponite, Na0.95Mg5.90[(Si7.07Al0.99)O20](OH)4

D 0.7075

A From Thien et al. (2012), their experimental compositions involving the AVM 6 glass 779 with the SGW at 219 days and 50 oC; concentration unit, 10–3 g•dm–3. 780

B This study, concentration unit, mol• dm–3; converted from the results of 781 Thien et al. (2012). The calculated total ionic strength for the solution is 0.14 mol• 782 dm–3. 783

C This study, concentration unit, mol•kg–1. Converted from the results on molar units by 784 using a density of 0.14 mol•dm–3 NaCl at 50 oC to approximate the density of the 785 SGW in which AVM 6 nuclear glass was corroded at 50 oC. The density of 0.14 786 mol•dm–3 NaCl at 50 oC is from Sőhnel and Novotný (1985). 787

788 D In , Q is ion activity product (IAP) with respect to saponite; K is the equilibrium 789

constant defined by Reaction (7). 790 791 792

Appendix A. The elements, their lowest limits of detection, or LLD (wt.%), the crystal 793 diffractometer used and counting times for EPMA analyses 794

795 Element 1-s LLD (wt.%) Crystal Counting time (s) Si 0.040 TAP A 20 sec Peak, 5 sec

Background Al 0.027 TAP 20 sec Peak, 5 sec

Background Mg 0.055 TAP 20 sec Peak, 5 sec

Background Na 0.050 TAP 20 sec Peak, 5 sec

Background A TAP, Thallium Acid Phthalate. 796

797

log QK

log QK

35

Appendix B. Comparison of major XRD peaks of saponite synthesized in this study with 798

those of the saponite 15 Å standard (PDF-00-013-0086)* 799

Mg-saponite Standard, PDF-00-020-0964 Saponite, Synthesized in this study

hkl d-spacing, Å Intensity hkl d-spacing, Å Intensity** (100) 4.57 50 (100) 4.572 166 (004) 3.67 60 (004) 3.666 214 (111) 2.58 20 (111) 2.577 242 (006) 2.42 20 (006) 2.421 217 (007) 2.09 30 (007) 2.089 82 (300) 1.53 90 (300) 1.534 111 (221) 1.32 40 (221) 1.322 76

*The major peaks with intensity ≥20 in the standard are compared with those in 800 the synthetic saponite. The significant numbers presented for d-spacing of the 801 synthesized saponite are one more than those presented in the PDF database for 802 comparison. It is obvious that the synthesized saponite has the identical d-803 spacings when its significant numbers are rounded as the same significant 804 numbers as the PDF database does. 805

** Experimental relative intensity 806 807 808 809 810 811 812

36

813 Figure 1. 814 815 816 817 818 819 820

821

0

250

500

750

1000

1250

1500

10 20 30 40 50 60 70 80 90

Rela

tive

Inte

nsity

2 theta

Saponite and nitrate cancrinite synthesized in this work

Standard PDF 00-013-0086, Saponite-15A, Mg3(Si, Al)4O10(OH)2•4H2O

Standard PDF 00-038-0531, NO3-Cancrinite, Na8[Al6Si6O24](NO3)2•4H2O

37

822

823 824

825 826 827 Figure 2A. 828

829

38

830 831

832 833 834 Figure 2B. 835 836

837

39

838 839

840 841 Figure 2C. 842 843 844 845 846

847

42

858

859 860 Figure 3. 861 862 863

864

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

50 60 70 80 90 100

Conc

entr

atio

n, m

olal

, mol

•kg-1

Experimental Time, Day

mOH- = 0.674 mol•kg-1

Mg

Al

Si

NO3–

Na